experimental evaluation and modeling of the hydrodynamics
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Experimental evaluation and modeling of thehydrodynamics in structured packing operated with
viscous waste oilsMargaux Lhuissier, Annabelle Couvert, A. Kane, Abdeltif Amrane, Jean-Luc
Audic, Pierre-Francois Biard
To cite this version:Margaux Lhuissier, Annabelle Couvert, A. Kane, Abdeltif Amrane, Jean-Luc Audic, et al.. Ex-perimental evaluation and modeling of the hydrodynamics in structured packing operated withviscous waste oils. Chemical Engineering Research and Design, Elsevier, 2020, 162, pp.273-283.�10.1016/j.cherd.2020.07.031�. �hal-02960344�
1
Experimental evaluation and modeling of the
hydrodynamics in structured packing operated with
viscous waste oils
Margaux Lhuissiera, Annabelle Couverta, Abdoulaye Kaneb, Abdeltif Amranea, Jean-Luc Audica, Pierre-
François Biarda
aUniv Rennes, Ecole Nationale Supérieure de Chimie de Rennes, CNRS, ISCR - UMR 6226, F-35000
Rennes, France
bUniLaSalle-Ecole des Métiers de l’Environnement, Campus de Ker Lann, 35170 Rennes, France
Graphical abstract:
Highlights:
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
0.5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
UG
(m s
-1)
L/G (kg kg-1)
Transformer oil flooding
0,8fl
0,6ufl
Loading zone (transformer oil)0.8×UG,Fl
0.6×UG,Fl
Air inlet
Air outlet
Structured Flexipac® packing
Experimental data for varying UG and UL
• Pressure drop• Loading points and flooding points
Modeling of the exp. data• Billet-Schultes
correlations
Predictive simulations using the Billet-Schultes correlations
• Loading and flooding points• Liquid holdup hL• Interfacial area a°• Pressure drop DP
Scale-up of an industrial column
• 4000 Nm3 h-1
• 1 ≤ L/G ≤ 5 kg kg-1
Viscous solventsPDMS 20 (20 mPa s)Transformer oil (19 mPa s)Lubricant (79 mPa s)
1 m
120 mmID
DP
Step 1
Step 2
Step 3
Step 4
Example
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Hydrodynamics of two waste oils and PDMS in a structured packing was investigated
Pressure drop in the loading zone was lower than 450 Pa m-1
Loading and flooding velocities were relatively low, especially using the viscous lubricant
Billet-Schultes correlations were efficient to predict the loading and flooding points and the
pressure drop
Scale-up calculations proved that transformer oil can be used in an industrial scale packed
column
Abstract :
The purpose of this work was to study the hydrodynamic behavior of two viscous waste oils (a
transformer oil and a lubricant characterized by viscosities of 19 mPa s and 79 mPa s, respectively)
and a silicone oil (20 mPa s) in a laboratory-scale packed column (Dcol = 0.12 m). The column was
filled with structured packing made of corrugated sheets (Flexipac® 500Z HC) and was operated at
counter-current. Thus, the gas superficial velocities at the loading point were in the range from 0.40 to
0.65 m s-1 for liquid loads between 1 and 24 m3 m-2 h-1, and, at the flooding point from 0.56 to 1.07 m
s-1 for liquid loads between 6 and 36 m3 m-2 h-1. Both loading and flooding points were particularly
influenced by the solvent viscosity, leading to a narrow loading zone for the most viscous solvent
(lubricant). The pressure drop values remained reasonable, lower than 450 Pa m-1 in the loading zone,
even for the lubricant. Billet-Schultes correlations were used for the prediction of the loading and
flooding velocities and of the pressure drop. The specific constants of the model were determined.
These correlations enable accurate predictions of the loading and flooding points, with an average
relative error around 7-8%, and of the pressure drop in the loading zone, with an average relative error
of 15%. Simulations were performed with the Billet-Schultes correlations and showed that high liquid
holdup and interfacial area would be obtained with these viscous solvents in the selected packing.
Scale-up calculations proved that it would be possible to implement the transformer oil at industrial
scale in a packed column filled with the studied structured packing.
Keywords: Absorption; Hydrodynamics; waste oils; PDMS; packed column; modeling
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Nomenclature
a: specific surface area of packing (m2 m-3)
ah : hydraulic surface area (Eq. 6 and Eq. 7, m2 m-3)
a°: interfacial area relative to the packing volume (m2 m-3)
ARE: Average Relative Error
CP, CLo, CFl, Ch : constants relative to each commercial packing according to Billet-Schultes
dh: hydraulic diameter = 4/a (m)
Dcol : column diameter (m)
F: volume flowrate (m3 h-1 or m3 s-1)
g: specific gravity constant (9.81 m s-2)
G: gas mass flowrate (kg s-1)
hL: liquid holdup (-)
L: liquid mass flowrate (kg s-1)
Re: Reynolds number (-)
U: superficial velocity (m s-1)
Z: packing height (m)
RE: Relative error
Greek letters
ΔP/Z : Linear pressure drop (Pa m-1)
: Packing void fraction (-)
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: resistance coefficient (-)
dynamic viscosity (Pa s)
density (kg.m-3)
Subscripts
L: Relative to the liquid phase
G: Relative to the gas phase
Lo: At the loading point
Fl: At the flooding point
1. Introduction
Volatile Organic Compounds (VOCs) have harmful effects on the environment through their global
warming contribution. Disturbing the Chapman cycle in the atmosphere by reacting with radicals,
VOCs cause tropospheric ozone accumulation and thus intensify global warming (Le Cloirec, 2004).
Besides, some VOCs could be toxic towards human health. Their impact on liver, blood and nervous
systems have been demonstrated (Kampa and Castanas, 2008).
Several mature technologies can be implemented to remove VOCs from air such as adsorption on
activated carbon filters, thermal and catalytic oxidations, absorption (gas-liquid scrubbing) or
biofiltration (Ruddy and Carroll, 1993). To target hydrophobic VOCs, absorption in a non-aqueous
phase (NAP) using silicone oils, phtalates, adipates or even ionic liquids, would be a promising
treatment (Hadjoudj et al., 2004; Heymes et al., 2006; Bourgois et al., 2006, 2009; Darracq et al.,
2010a; Darracq et al., 2010b; Guihéneuf et al., 2014; Biard et al., 2016, 2018; Rodriguez Castillo et
al., 2018, 2019). Nonetheless, all these commercial or laboratory made solvents are very expensive,
which would increase the CAPEX of an industrial process. Consequently, several studies have
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recently investigated the potential of cheaper NAP, such as waste oils (Bay et al., 2006; Lalanne et al.,
2008; Ozturk and Yilmaz, 2006).
In a previous paper investigating the physico-chemical properties (viscosity, volatility, partition
coefficient for toluene and dichloromethane) of several industrial waste oils (Lhuissier et al., 2018),
lubricant and transformer oil were proved to be potential NAP candidates for VOC absorption.
Nevertheless, these waste oils are from 10 to 70 times more viscous than water and have a low
surface tension, which can affect significantly their hydrodynamics, especially in irrigated packed
columns which are the most commonly used contactors at industrial scale for gas scrubbing (Le
Cloirec, 2004; Minne, 2017).
In a counter-current packed column, it is recommended to operate in the loading zone located
between the loading and flooding points (Billet and Schultes, 1999). Indeed, for gas velocities below
the loading points (in the pre-loading zone), the downward flow of liquid, and consequently the liquid
holdup, depend only on the liquid rate and are not influenced by the gas velocity, leading to low
interfacial area and gas-liquid interactions (Billet and Schultes, 1999, 1995, 1993; Heymes et al.,
2006; Mackowiak, 2010; Stichlmair et al., 1989). In this pre-loading zone, the pressure drop increases
linearly with the gas superficial velocity (Piché et al., 2001a). In the loading zone, the shear forces in
the gas flow support some of the descending liquid allowing to increase advantageously the liquid
holdup and the interfacial area (Billet and Schultes, 1999; Piché et al., 2001a). In the loading zone, the
pressure drop increases with the gas superficial velocity to a power of around 1.8 (Piché et al., 2001a).
Then, when the flooding point is reached, the shear stress of the gas flow is high enough to maintain
the liquid at the top of the column, i.e. the liquid starts to overflow and the pressure drop increases
sharply (Billet and Schultes, 1999, 1995, 1993; Piché et al., 2001b). Consequently, for a given gas
flowrate, the choice of a working point in the loading zone allows subsequently to determine the
diameter of the contactor (Roustan, 2003). More precisely, a working gas superficial velocity equal to
70-80% of the flooding velocity is recommended by several authors (Billet and Schultes, 1999;
Maćkowiak, 1991), even if a lower boundary of 60% was also proposed (Roustan, 2003).
Several semi-empirical correlations have been developed in the literature to determine the loading and
flooding points as-well-as liquid holdup and pressure drop in the pre-loading and loading zones of
either random and structured packing (Maćkowiak, 1990, 1991; Miyahara et al., 1992; Rocha et al.,
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1993; Billet and Schultes, 1999; S. Piché et al., 2001a, 2001b, 2001c; Heymes et al., 2006). These
correlations take into account the column diameter, packing characteristics (porosity, particle diameter,
specific surface area, etc.), liquid and gas properties (viscosity, density, superficial tension) and liquid-
to-gas mass flowrate ratio L/G. Besides, the pressure drop in the loading zone depends also on the
selected liquid and gas velocities. Most of these correlations were established using data gathered
with water-like solvents having low or moderate viscosities. The Billet-Schultes correlations were
developed in the 90ties for both random and structured packing with solvents having dynamic velocities
up to around 100 mPa s (Billet and Schultes, 1999, 1993). In 2006, Heymes et al. showed that these
correlations were the most accurate to predict the pressure drop of dumped packing using DEHA. In
2017, Minne also proved the good predictive capacity of these correlations using solvents with
different viscosities, densities and surface tension (ethylene glycol, silicone oil, water and Isopar G).
The procedure developed by Billet-Schultes involves the calculation of liquid holdup, which is the ratio
of the liquid within the column volume to the packing volume.
Only a few studies have been performed to assess the hydrodynamics of viscous solvents in packed
columns, and up to now, no one has been dedicated to waste oils (Brunazzi et al., 2002; Darracq,
2011; Guillerm et al., 2016; Heymes et al., 2006; Minne, 2017; Minne et al., 2018; Tsai et al., 2009).
Thus, the purpose of this work is to study the hydrodynamics of two waste oils, a lubricant and a
transformer oil, in a laboratory scale packed column, by comparison to another reference solvent: a
commercial silicone oil (PDMS 20). A modern 4th generation structured packing made of metallic
corrugated sheets was used (Flexipac® 500Z HC). Both the loading and flooding points for several
liquid-to-gas mass flowrate ratios (L/G) have been determined, as well as the pressure drop evolution
with the gas and liquid velocities. Besides, the reliability of the Billet-Schultes correlations was
evaluated allowing to subsequently simulate different conditions and to assess the scale-up of the
process at industrial scale.
2. Material and method
2.1 Chemical products
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The silicone oil used was composed of polydimethylsiloxane (PDMS), a synthetic oil named Rhodorsil
47V20 provided by Bluestar Silicones (Table 1). The waste oils were selected among those collected
by Chimirec (Javené, France).
2.2 Pilot-scale packed column
The irrigated packed column (120 mmID (Dcol) and packing height Z of 1 m) was operated at counter
current (Fig. 1). The air flow (G = 1.17 kg m-3 at 25°C and 1 atm) was introduced at the bottom of the
column and the liquid solvent was introduced at the top of the column. The column was filled with
structured packing (Flexipac®, provided by Koch Glitsch-USA) made out of corrugated sheets
arranged in a crisscrossing configuration to create flow channels for the gas phase (Table 2).
The air flowrate was regulated by means of a membrane valve located after a fan and measured by a
rotameter (GF Type SK 20 CH-8201, Switzerland). The column was fed with the liquid absorbent by
means of a centrifugal pump (Iwaki MD100, Japan). The liquid flowrates were regulated with a valve
and measured by a previously calibrated rotameter (GF type SK 11 CH-8201, Switzerland). The
experimental conditions and the range of operating parameters are shown in Table 3. For each liquid
flowrate selected, the gas flow was increased incrementally up to the flooding point (determined by
visual observation), and pressure drops (ΔP) were measured three times for each point using a
vertical U-shaped tube filled with water. Only the pressure drop corresponding to the packing was
measured. The temperature of the liquid phase ranged from 294 to 298 K, and the gas temperature
was kept constant at 298 K by means of a heat exchanger. Considering all the experiments, the
difference between the inlet temperatures of the gas and liquid phases was always lower than 3 K.
The accuracy and reliability of this set-up was previously checked by Darracq and Guillerm (Darracq,
2011; Guillerm, 2017).
Billet-Schultes correlations Billet and Schultes (B-S) developed a set of correlations allowing to determine (i) both the loading and
flooding gas superficial velocities (UG,Lo and UG,Fl) for a given L/G ratio and (ii) the pressure drop, liquid
holdup and the interfacial area for the selected working gas superficial velocity (UG) in both the pre-
loading and loading zones (Billet and Schultes, 1999, 1995, 1993, 1991). These correlations,
presented in Table 4, involve several constants which depend specifically on the packing (CP, CLo, CFl
and Ch). The structured packing used in this study was not previously tested by Billet-Schultes.
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Therefore, the constants used in our calculations were deduced from the experimental results (part
3.3). For a given packing, the loading and flooding points depend on the selected L/G ratio, the liquid
and gas properties and the packing properties. They can be deduced from the equations 1-7 and 8-11,
respectively. These sets of equations need to be solved by iteration (for example using the Excel®
Solver). The determination of the loading points involved the determination of the ratio of the hydraulic
to the geometric surface area (ah/a) according to Eqs. 6 or 7. This ratio must not be confused with the
ratio of the specific interface between the phases to the geometric area (a°/a), determined with Eqs.
18-20. Besides, these equations involve several resistance coefficients () whose calculation depends
on the nature of the dispersed phase (Eqs. 3-4 and Eqs. 10-11).
3. Results and Discussion
3.1 Experimental pressure drop of the irrigated column
The experimental pressure drop of the irrigated packed column increases logically with both the liquid
and gas superficial velocities according to Fig. 2. The gas velocity can be easily converted to the vapor
capacity factor FV, often used to report data dealing with the hydrodynamics of an irrigated packed
column (Minne, 2017), by multiplication with the square root of the air density (which was almost
constant in this study and equal to 1.17 kg m-3). Lower liquid velocities were applied for the lubricant
since the flooding was reached at a lower L/G ratio for a given gas velocity than for silicon and
transformer oils. This observation is consistent with the fact that both loading and flooding points
appear at lower gas velocities for viscous solvents at similar liquid densities (Minne, 2017).
Nonetheless, even with a high viscosity, it would be feasible to use this lubricant in a packed column.
In Fig. 2, experimental points located in both pre-loading and loading zones are represented. Some
values of the pressure drop were also measured in the flooding zone but are not represented in Fig. 2
for clarity. In the pre-loading zone, the pressure drop increases linearly with the gas velocity and is
minimally influenced by the nature and the flowrate of the liquid. Minne (2017) and Brunazzi et al.
(2002) also observed this behavior for various liquids with similar densities but very different
viscosities for random and structured packing, respectively. It is consistent with the fact that gas and
liquid have almost no interaction in the pre-loading zone. However, this behavior completely changes
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when the loading point is reached. Indeed, the pressure drop at given liquid and gas velocities is
significantly higher for the lubricant in the loading zone than for the transformer oil and the silicon oil.
Furthermore, the pressure drop increases with the gas velocity to the power of 1.8. All these
observations in the loading zone are in agreement with the literature (Minne, 2017; Minne et al., 2018;
Piché et al., 2001a). The results emphasize that the pressure drop values stay advantageously under
450 Pa.m-1 in both the pre-loading and loading zones for each of the viscous liquid phases, showing
that the implementation of viscous solvents would not affect significantly the operating costs (OPEX).
However, the results clearly show that lower L/G ratios must be selected when the solvent viscosity
increases to avoid loading and flooding points that would be too low, highlighting that the
determination of the loading and flooding points would be determinant when designing a column. To
reach this goal, robust models must be implemented.
3.2 Determination of the experimental loading and flooding
points
The log-log plots corresponding to Fig. 2 are provided as supplementary material (Fig S.1). For the
three solvents, the experimental loading and flooding superficial velocities, summarized in Table 5 and
Table 6, were determined from the break-up of the slopes between the pre-loading zone, the loading
zone and the flooding zone on these log-log plots.
The loading and flooding points for a given liquid-to-gas mass flowrate ratio (L/G) were close to the
results obtained previously by Guillerm et al. (2016) with the same packing using PDMS 50 (viscosity
of 50 mPa.s). The observed loading and flooding velocities are relatively low, in the range 0.39-0.65
and 0.56-1.06 m s-1, respectively. This behavior is justified by both the nature of the packing, which is
a structured packing with a high interfacial area leading to a high liquid capacity, and the high viscosity
of the solvents investigated.
Indeed, in agreement with the experimental observations and theoretical considerations of other
authors (Billet and Schultes, 1995; Brunazzi et al., 2002; Minne et al., 2018), both loading and flooding
velocities decreased with the solvent viscosity because of higher frictional forces. Thus, lower liquid
loads were operated for the most viscous solvent, i.e. the lubricant. Nonetheless, having similar
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viscosities, densities and surface tensions, the loading and flooding velocities for the transformer oil
and the silicon oil are not significantly different at a given liquid load. On the one hand, the influence of
the density on the hydrodynamics is rather well described in the literature. Indeed, the gravitational
forces are counterbalanced by the frictional forces at lower velocities when the density decreases
(Minne, 2017). On the other hand, the possible influence of the surface tension is still controversial in
the literature and seems to depend on the nature of the packing and of the liquid load (Minne, 2017).
Anyway, the Billet-Schultes model, applied in the next part, does not take the influence of the surface
tension into account.
3.3 Application of the Billet-Schultes: determination of the
specific constants for Flexipac® 500Z HC packing.
Eqs 8-11 show that the determination of the flooding point at a given L/G ratio depends on the
properties of the liquid phase (viscosity and density ) and on the properties and the nature of the
packing through its void fraction , specific area a and through a specific constant CFl. By trying to
minimize the sum of the relative errors (RE) between the experimental gas flooding velocities and
those deduced from the B-S correlations, the value of CFl was determined (Table 7). The value found
is in agreement with the range previously determined by Billet and Schultes (Billet and Schultes,
1999). The low average relative error (ARE) of 7.5% (calculated for 11 values) between the
experimental and theoretical gas flooding velocities (summarized on Table 6) shows that B-S
correlations are efficient for the prediction of the flooding points even for solvents with very different
properties. Minne (2017) found similar RE for a silicon oils using two dumped packing. The parity plot
is provided as supplementary material and does not put in evidence any systematic error (Fig. S-2(b)).
From Eqs 8-11, the liquid holdup at the flooding points was also determined (Table 6).
Eqs. 1-7 show that the determination of the loading point at a given L/G ratio depends on the
properties of the liquid phase (viscosity and density ) and on the properties and the nature of the
packing through its void fraction , specific area a and through two specific constant CLo and Ch.
Several couples (CLo ;Ch) allowed to minimize the ARE between the experimental gas loading
velocities and those deduced from the B-S correlations. Thus, the best couple summarized on Table 7
was determined through the simultaneous minimization of the ARE of both the experimental and
theoretical pressure drops and loading points. Only the pressure drops measured in the loading zone
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were considered. Indeed, the pressure drop in the pre-loading zone is low and suffers from higher
experimental uncertainties. Besides, Minne (2017) pointed out the relatively low performance of the
Billet-Schultes model to predict the pressure drop on the pre-loading zone.
The values of Ch and CLo found are in agreement with the ranges previously determined by Billet and
Schultes (Billet and Schultes, 1999), even if the value of CLo is slightly lower than the range of Table 7.
The low ARE of 8.0% (calculated for 10 values) between the experimental and theoretical gas loading
velocities (summarized on Table 5) shows that the B-S correlations are efficient for the prediction of
the loading points, even for solvents with very different properties. The parity plot is provided as
supplementary material and shows that the model slightly overestimates the loading points for the
lubricant and slightly underestimates them for the transformer oil (Fig. S-2(a)), but these discrepancies
remain acceptable.
The results summarized in Table 5 and Table 6 clearly confirm that the liquid holdup would be higher
at a given L/G ratio for the lubricant, i.e. for a higher viscosity, for both the loading and flooding points.
Thus, even if viscous solvents must be operated at a lower superficial gas velocity and/or a lower L/G
ratio (i.e. lower absorption rate (Biard et al., 2018)), a higher interfacial area would be expected.
Finally, the value of Cp (Table 7) was determined through the minimization of the ARE between the
experimental and theoretical (Eqs 12-17) pressure drops of the points located in the loading zones.
The value of Cp found is in agreement with the range previously determined by Billet and Schultes
(Billet and Schultes, 1999). The low average relative error of 15.1% (calculated for 134 values: 42 for
PDMS 20, 32 for transformer oil, 60 for lubricant) between the experimental and theoretical pressure
drops in the loading zone shows that B-S correlations estimate with a good confidence level the
pressure drop even with viscous solvents. On the pre-loading zone, the agreement is lower, with an
ARE of 34.1%, which is consistent with the observations of Minne (2018). Nonetheless, it is not
recommended to operate on the pre-loading zone (Billet and Schultes, 1999). The agreement between
the experimental and theoretical pressure drops on the pre-loading and loading zones can be
assessed Fig. 2. The detailed ARE for the three solvents in each zone are summarized in Table 8. It
shows that the best agreement is found for PDMS 20 and transformer oil. For the lubricant, the ARE is
higher, around 27%, but remains fully acceptable. Furthermore, the parity plot of the pressure drop is
provided as supplementary material and does not put in evidence any systematic error (Fig. S-3).
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3.4 Discussion and simulations
From the constants determined previously (Table 7) and the B-S correlations, it was possible to
estimate the loading and flooding points for the two waste oils for an increasing L/G ratio in the 0.5-15
range (Fig. 3).
The loading and flooding velocities obviously decrease with the L/G ratio. For the lubricant (i.e. the
most viscous solvent), the loading velocity is from 6% (at L/G = 0.5) to 20% higher (at L/G = 15) and
the flooding velocity is from 10% (at L/G = 0.5) to 30% higher (at L/G = 15) than for the transformer oil.
Because of almost identical properties, the data for PDMS 20 are similar to those of the transformer oil
and are not represented. For the sake of comparison, a simulation for water was also carried out (Fig.
S-4). The results show that for this solvent, the loading and flooding points would be respectively from
17 to 52% higher and from 25 to 48% higher than for the transformer oil.
Fig. 3 shows that the choice of a working velocity at 80% of the flooding velocity allows operating in
the loading zone in any case. However, the choice of a working velocity at 60% of the flooding
velocity, proposed as a lower boundary by some authors (Roustan, 2003), would be inappropriate,
especially at high L/G ratio and for the lubricant. The breakthrough of the curves observed at a L/G
ratio around eleven is due to a shift of the dispersed phase (from the liquid to the gas phase)
corresponding to a value of 𝐿
𝐺× √
𝜌𝐺
𝜌𝐿 higher than 0.4 (Table 4).
Fig. 3 also highlights that the selection of an excessive L/G ratio would be inappropriate for several
reasons. Indeed, for the viscous solvents investigated, it would impose to select a low superficial gas
velocity, i.e. to increase the column diameter for a given gas flowrate to treat. Moreover, a low
superficial gas velocity would affect the turbulences in the gas phase, decreasing the gas-phase mass
transfer rate. Since a significant part of the mass transfer resistance can be located in the gas phase
during hydrophobic VOC absorption, even using viscous solvents (Biard et al., 2018; Rodriguez
Castillo et al., 2019), would decrease the overall mass transfer rate. Finally, for a high L/G ratio, the
loading zone is narrower. Thus, low variations of the gas velocity may induce significant variations of
the hydrodynamics within the column, which would complicate the monitoring of a packed column at
industrial scale.
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The evolution of the pressure drop DP/Z (orange curves), the liquid holdup hL (yellow curves) and the
ratio a°/a was simulated for several liquid loads (Fig. 4). hL and the ratio a°/a remain constant in the
pre-loading zone in agreement with the experimental observations of several authors with structured
packing (Billet and Schultes, 1993; Brunazzi et al., 2002; Zakeri et al., 2012). In the pre-loading zone,
hL and the ratio a°/a increase by 100% for the transformer oil when the liquid load increases by a
factor of 4 (from 5 to 20 m h-1). Moreover, hL and the ratio a°/a are around 30% higher for the lubricant
in the pre-loading zone. Brunazzi et al. (2002) also showed that the liquid holdup increases with the
solvent viscosity even in the pre-loading zone. Thus, a viscous solvent exhibits advantageously a
higher interfacial area although the pressure drop is almost insensitive to the nature of the solvent, at
least in the pre-loading zone.
When the loading zone is reached (around 0.60 m s-1 for UL = 5 m h-1 and around 0.45 m s-1 for UL =
20 m h-1 for the transformer oil; around 0.55 m s-1 for UL = 5 m h-1 for the lubricant), the gas and the
liquid start to interact. Thus, both hL and the ratio a°/a increase until the flooding point is reached
(around 1.20 m s-1 for UL = 5 m h-1 and around 0.78 m s-1 for UL = 20 m h-1 for transformer oil; around
1.02 m s-1 for UL = 5 m h-1 for the lubricant). A rather high liquid holdup, from 25 to more than 45%,
would be reached at the flooding point. High liquid hold ups are concomitant with a good wetting of the
column and with high interfacial area a°. The interfacial area can be even higher that the geometrical
area a of the packing according to the experimental observations of Tsai et al. (2009) on similar
structured packing fed with solvents having viscosities up to 14 mPa s. Cherif et al. (2017) showed the
good predictive capacity for a° of the Billet-Schultes correlations for a structured packing. In the
loading zone, contrarily to the pre-loading zone, the pressure drop is particularly sensitive to the liquid
load and the viscosity of the solvent. Thus, for example, at a liquid load of 5 m h-1 and a gas velocity of
0.8 m s-1, the interfacial area and the pressure drop for the lubricant would be around 40% and 15%
higher than for the transformer oil, respectively.
3.5 Packing scale-up
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According to part 3.3, the Billet-Schultes correlations provide fair estimations of the pressure drop and
loading and flooding points. These parameters are crucial for the evaluation of the operating cost
through the determination of the packed column diameter and the selection of the L/G ratio (part 3.4).
In this part, in order to study the scale-up of a column with this specific packing, a realistic case
involving a flowrate of 4000 Nm3.h-1 of air to be treated was considered (where N stands for the
standard temperature and pressure (STP) conditions, meaning 1 bar and 0°C according to the
IUPAC). The transformer oil was selected among the three solvents considering the observations of
the parts 3.3 and 3.4. Biard et al. (Biard et al., 2018; Rodriguez Castillo et al., 2019) already studied
the hydrodynamics of DEHA (12.5 mPa s), PDMS (50 mPa s) and two ionic liquids (50-60 mPa s) in a
packed column (Dcol = 1 m) filled with bulk Pall® rings for with the same gas flowrate using the Billet-
Schultes correlations. Apart from a different packing nature (corrugated sheets vs. random rings),
Pall® rings offer a geometric surface area of only 139.4 m2 m-3, around 3 times lower than
Flexipac®500 Z HC. Thus, both the computed loading and flooding superficial velocities for similar L/G
ratio (in the range 1-5) are significantly lower with the Flexipac® packing. Thus, it was impossible to
select the same working velocity of 1.52 m s-1 as Biard et al. (Biard et al., 2018; Rodriguez Castillo et
al., 2019) since this one is higher than the computed flooding velocity for the Flexipac® packing
whatever the L/G ratio considered.
Thus, for this scale-up assessment, a L/G ratio in the range 1-5 to avoid flooding velocities that were
too low (Fig. 3 (a)) was selected. Then, a working gas velocity taken at 80% of the flooding velocity as
recommended in the literature was considered (Billet and Schultes, 1999). A working gas velocity
(which decreases with the L/G ratio), in the range 0.54-0.86 m s-1, and a column diameter (which
increases with the L/G ratio), in the range 1.33-1.68 m, were calculated. Fig. 5 presents the evolution
of the liquid holdup hL, interfacial area a° and pressure drop DP/Z calculated with the B-S correlations
for increasing L/G ratios.
The calculated pressure drops would be in a reasonable range (95-175 Pa m-1) for an industrial
application. The pressure drop would be lower at industrial scale at given liquid and gas velocities than
at the lab-scale, because of negligible wall effects. These wall effects are taken into account by the
Billet-Schultes correlations through the column diameter (Eqs. 15-17). The pressure drop decreases
with the L/G ratio and with the working gas velocity UG, even if the liquid holdup and the liquid load
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increase. The low values of the pressure drop must be balanced with the low gas velocity tolerated by
this packing. It confirms that viscous solvents do not necessarily lead to high pressure drop (Biard et
al., 2018). Advantageously, the computed interfacial area is significant, higher than 200 m2 m-3. These
results emphasize the good hydrodynamic performance offered by this packing. Nonetheless, the use
of a low gas velocity would be detrimental for the mass transfer rate in the gas phase, in which the
main part of the resistance can be located, especially during the absorption of hydrophobic VOCs for
which the selection of viscous absorbents is justified (Rodriguez Castillo et al., 2019).
4. Conclusion
The purpose of this work was to study the hydrodynamic behavior of two viscous waste oils (a
transformer oil and a lubricant characterized by viscosities of 19 mPa s and 79 mPa s, respectively)
and a silicone oil (20 mPa s) in a laboratory-scale packed column (Dcol = 0.12 m) filled with structured
packing (Flexipac® 500Z HC). First, the results showed that it was possible to successfully apply such
viscous solvents in structured packing made of corrugated sheets. The loading and flooding points
were determined for L/G ratios between 0.3 and 14.0. Pressure drop in the loading zone values were
in the range from 50 to 450 Pa.m-1. The pressure drop values were significantly higher in the loading
zone at the same gas and liquid velocities for the most viscous solvent (lubricant) than for the other
solvents. Besides, lower liquid loads (i.e. liquid velocities) must be applied for the lubricant, since the
flooding point was reached at lower gas velocities for a given L/G ratio. Considering that the high
lubricant viscosity will also lower the mass transfer rate (directly, through lower turbulences, and
indirectly, through lower diffusion coefficients (Rodriguez Castillo et al., 2019)), the selection of such a
viscous solvent would be justified only for pollutant/solvent systems characterized by low partition
coefficient (i.e. high affinities).
In order to apply waste oils in a scrubbing process, the accurate prediction of the hydrodynamic
performance is a prerequisite. The Billet-Schultes correlations (Billet and Schultes, 1999) were used to
predict the loading points and flooding points, as well as the pressure drop, the liquid holdup and the
interfacial area at the working velocity. The specific constants of the packing used were determined by
numerical resolution. The ARE between the experimental and theoretical pressure drops in the loading
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zone was around 15%. Furthermore, the Billet-Schultes correlations successfully determined the
loading and flooding points with ARE around 7-8%. Several simulations were performed with these
correlations to assess the influence of the operating conditions. It highlighted the high hydrodynamic
performance of this packing. It also demonstrated that the use of viscous solvents does not
necessarily lead to excessive pressure drop in agreement with the experimental results. A fortiori, high
liquid holdup and interfacial area would be advantageously obtained. Nonetheless, low loading and
flooding velocities were computed, even for a low L/G ratio, which leads to select low working gas
velocities, leading to high diameter columns and lowered mass transfer rate in the gas phase. Finally,
the scale-up of a realistic packed column for gas treatment was assessed and showed that that it
would be possible to apply these kinds of solvents with the Flexipac®500Z HC packing even at
industrial scale. For a complete techno-economic assessment, the determination of the mass transfer
coefficients in both the liquid and gas phases will be necessary, allowing to evaluate concomitantly the
pressure drop, the overall mass transfer coefficient and thus, the resulting removal efficiency in a
given packed column (Biard et al., 2018; Rodriguez Castillo et al., 2019).
5. Acknowledgments
We are very grateful to the French Association Nationale de la Recherche et de la Technologie
(ANRT) for the CIFRE PhD grant N° 2016/0238 attributed to Margaux Lhuissier, and also to the
French governmental agency ADEME for the CORTEA funding n°1881C0001. We would like to thank
our industrial partner Chimirec for providing the waste oils used in this study. We would like to give a
warm thanks to Thomas HULL (UniLaSalle-Ecole des Métiers de l’Environnement) for proofreading
this article.
Declaration of interests
The authors declare that they have no known competing financial interests or personal relationships that
could have appeared to influence the work reported in this paper.
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Figure 1: Experimental set-up.
Figure 2 : Evolution of the pressure drop with the gas velocity for PDMS (a), transformer oil (b) and
lubricant (c) for increasing values of the liquid load UL (in m3 m-2 h-1). The straight lines correspond to the
calculations according to the Billet-Schultes correlations (part 3.3).
Air
Fan
T P F
DP
Centrifugal pump
Solvant tank
U-tube filledwith water
Heat exchanger
Packed column(120 mm ID, packing height = 1 m
Flexipac® packing)
Air outlet
T
F
0
50
100
150
200
250
300
350
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
DP/
Z (P
a m
-1)
UG (m s-1)
1.4
2.7
4.0
5.2
6.5
7.7
8.9
Loading
0
50
100
150
200
250
300
350
400
450
0.0 0.2 0.4 0.6 0.8 1.0 1.2
DP/
Z (P
a m
-1)
UG (m s-1)
4.3
9.9
16.1
22.79
29.8
37.1
Loading
Flooding
0
50
100
150
200
250
300
350
400
0.0 0.2 0.4 0.6 0.8 1.0 1.2
DP/
Z (P
a m
-1)
UG (m s-1)
3.1
7.4
12.4
17.8
23.7
29.8
36.3
Loading
Flooding
(a) PDMS 20 (b) Transformer oil (c) Lubricant
UL (m h-1) UL (m h-1) UL (m h-1)
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Figure 3: Evolution of the loading and flooding gas velocity for transformer oil (a) and lubricant (b) for
increasing values of the L/G ratio (Flexipac® 500Z HC). The green frame corresponds to the loading zone
(located between the loading and the flooding velocities). The orange and blue lines correspond to 80%
and 60% of the flooding velocity, respectively. These data were simulated using the B-S correlations.
Figure 4: Evolution of the pressure drop (orange curves), the liquid holdup (yellow curves) and the ratio
a°/a (green curves) for increasing values of the gas velocity for transformer oil (a) and lubricant (b)
(Flexipac® 500Z HC). Two liquid loads (5 and 20 m h-1) were simulated for the transformer oil and one
liquid load (5 m h-1) was simulated for the lubricant. These data were simulated using the B-S
correlations.
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
0.5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
UG
(m s
-1)
L/G (kg kg-1)
Lubricant flooding
0,8fl
0,6ufl
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
0.5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
UG
(m s
-1)
L/G (kg kg-1)
Transformer oil flooding
0,8fl
0,6ufl
(a) (b)
Loading zone (transformer oil)0.8×UG,Fl
0.6×UG,Fl
Loading zone (lubricant)0.8×UG,Fl
0.6×UG,Fl
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
110%
120%
0
50
100
150
200
250
300
350
400
450
500
550
600
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
hL
and
a0 /
a
DP/
Z (P
a m
-1)
UG (m s-1)
DP/Z
hL
a°/a
0%
15%
30%
45%
60%
75%
90%
105%
120%
135%
150%
0
50
100
150
200
250
300
350
400
450
500
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
hL
and
a0 /
a
DP/
Z (P
a m
-1)
UG (m s-1)
DP/Z
DP/Z
hL
a°/a
hL
a°/a
(a) (b)
DP/ZhLa°/a
DP/ZhLa°/a
DP/ZhLa°/a
UL = 5 m h-1
UL = 5 m h-1
UL = 20 m h-1
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Figure 5: Evolution of the pressure drop (black curve), the liquid holdup (orange curve), the interfacial
area a° (purple curve), the column diameter (green curve) and the liquid (blue curve) and gas (red curve)
velocities for increasing values of the L/G ratio for the transformer oil for the following design: FG = 4000
Nm3 h-1, UG = 0.80×UG,Fl, using Flexipac® 500Z HC and G = 1.17 kg m-3.
0
40
80
120
160
200
240
280
320
360
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
1 2 3 4 5
DP/
Z (P
a m
-1);
uL
(m h
-1) a
nd
a°
(m2 m
-3)
UG
(m s
-1);
Dco
l(m
) an
d h
L
L/G (kg kg-1)
UG
Dcol
hL
UL
a°
DP
Dcol
a°
UG
DP/Z
hL
UL
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Table 1: Properties of the studied liquid absorbents.
PDMS Transformer oil Lubricant
Chemical composition Siloxanes Linear alkanes
Dynamic viscosity L (mPa s) at 25°C 20 19 79
Molar mass (g mol-1) 3000 212*
Density L (kg m-3) 900 865 875
Superficial tensionL (N m-1) 0.021 0.027 0.031
* Lubricant and transformer oil have complex chemical structures. Several samples were investigated by 1H-NMR spectroscopy and showed quite similar chemical natures between lubricant and transformer oil and allowed to roughly estimate an average chain length of 15 carbons which is coherent with literature data for mineral oils (Aluyor and Ori-jesu, 2009).
Table 2: Packing characteristics
Name dh (m) a (m−1) ε (-)
Flexipac® 500Z HC 7.60.10-3 500 0.95
Table 3: Operating conditions
P T D Z FG FL UG UL
bar °C m m Nm3 h-1 L h-1 m s-1 m s-1
1 25 0.12 1 9 – 50 15 – 750 0.2 – 1.2 3.10-4 – 2.10-2
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Table 4: Billet-Schultes correlations developed for the determination of the parameters relative to the
hydrodynamics of an irrigated counter-current packed column (Billet and Schultes, 1999, 1995, 1993,
1991).
Determination of the loading point (UG,Lo) for a given L/G ratio
𝑈𝐺,𝐿𝑜 = √𝑔
𝜓𝐿𝑜× (𝜀 − ℎ𝐿,𝐿𝑜) × √
ℎ𝐿,𝐿𝑜
𝑎× √
𝜌𝐿
𝜌𝐺
𝑈𝐿,𝐿𝑜 =𝜌𝐺
𝜌𝐿
×𝐿
𝐺× 𝑈𝐺,𝐿𝑜
With:
𝜓𝐿𝑜 =𝑔
𝐶𝐿𝑜2 × (
𝐿
𝐺.√
𝜌𝐺
𝜌𝐿(
𝜇𝐿
𝜇𝐺)
0.4
)0,752
if 𝐿
𝐺× √
𝜌𝐺
𝜌𝐿≤ 0.4 (liquid dispersed in the gas)
𝜓𝐿𝑜 =𝑔
(0.695𝐶𝐿𝑜(𝜇𝐿𝜇𝐺
)0.1588
)
2 × (𝐿
𝐺√
𝜌𝐺
𝜌𝐿(
𝜇𝐿
𝜇𝐺)
0.4
)1,46
if 𝐿
𝐺× √
𝜌𝐺
𝜌𝐿> 0.4 (gas dispersed in the
liquid) And:
ℎ𝐿,𝐿𝑜 = (12
𝑔
𝜇𝐿
𝜌𝐿
𝑎2𝑈𝐿,𝐿𝑜)1 3⁄
× (𝑎ℎ
𝑎)
2 3⁄
With:
(𝑎ℎ
𝑎) = 𝐶ℎ × (
𝑈𝐿,𝐿𝑜.𝜌𝐿
𝑎.µ𝐿)
0.15
× (𝑈𝐿,𝐿𝑜
2.𝑎
𝑔)
0.1
if (𝑈𝐿,𝐿𝑜.𝜌𝐿
𝑎.µ𝐿) < 5
(𝑎ℎ
𝑎) = 0.85 × 𝐶ℎ × (
𝑈𝐿,𝐿𝑜.𝜌𝐿
𝑎.µ𝐿)
0.25
× (𝑈𝐿,𝐿𝑜
2.𝑎
𝑔)
0.1
if (𝑈𝐿,𝐿𝑜.𝜌𝐿
𝑎.µ𝐿) ≥ 5
Eq. 1 Eq. 2 Eq. 3 Eq. 4 Eq. 5 Eq. 6 Eq. 7
Determination of the flooding point (UG,Fl) for a given L/G ratio
ℎ𝐿,𝐹𝑙3 . (3. ℎ𝐿,𝐹𝑙 − 𝜀) =
6
𝑔. 𝑎2. 𝜀.
𝜇𝐿
𝜌𝐿
.𝐿
𝐺.𝜌𝐺
𝜌𝐿
. 𝑈𝐺,𝐹𝑙
With:
𝑈𝐺,𝐹𝑙 = √2. 𝑔
𝜓𝐹𝑙
×(𝜀 − ℎ𝐿,𝐹𝑙)
1.5
𝜀0.5× √
ℎ𝐿,𝐹𝑙
𝑎× √
𝜌𝐿
𝜌𝐺
And:
𝜓𝐹𝑙 =𝑔
𝐶𝐹𝑙2 . (
𝐿
𝐺√
𝜌𝐺
𝜌𝐿(
𝜇𝐿
𝜇𝐺)
0.2
)0,388
if 𝐿
𝐺× √
𝜌𝐺
𝜌𝐿≤ 0.4
𝜓𝐹𝑙 =𝑔
(0.6244𝐶𝐹𝑙(𝜇𝐿𝜇𝐺
)0.1028
)
2 × (𝐿
𝐺√
𝜌𝐺
𝜌𝐿(
𝜇𝐿
𝜇𝐺)
0.2
)1.416
if 𝐿
𝐺× √
𝜌𝐺
𝜌𝐿> 0.4
Eq. 8 Eq. 9 Eq. 10 Eq. 11
Determination of the holdup (hL) at the working point (UG < UG,Fl and
𝑼𝑳 =𝝆𝑮
𝝆𝑳.
𝑳
𝑮. 𝑼𝑮)
Step 1: hL,Lo from Eqs. 5-7 and calculated with UL
Step 2: ℎ𝐿,𝐹𝑙 = 2.2ℎ𝐿,𝐿𝑜 (𝜇𝐿𝜌𝑊
𝜇𝑊𝜌𝐿)
0.05
Step 3: ℎ𝐿 = ℎ𝐿,𝐿𝑜 + (ℎ𝐿,𝐹𝑙 − ℎ𝐿,𝐿𝑜) × (𝑈𝐺
𝑈𝐺,𝐹𝑙)
13
(with hL,Lo and hL,Fl from steps 1 and 2)
Eq. 12 Eq. 13 Eq. 14
Determination of the pressure drop (DP/Z) at the working point
𝛥𝑃
𝑍= 𝜓𝐿 ×
𝑎
(𝜀 − ℎ𝐿)3×
𝑈𝐺2𝜌𝐺
2× (1 +
4
𝑎𝐷𝑐𝑜𝑙
)
With:
𝜓𝐿 = 𝐶𝑃 × (64
𝑅𝑒𝐺+
1.8
𝑅𝑒𝐺0.08) × 𝑒𝑥𝑝 (
13300
𝑎. √
𝑈𝐿2
𝑔) × (
𝜀−ℎ𝐿
𝜀)
1.5
× (ℎ𝐿
ℎ𝐿,𝐿𝑜)
0.3
with hL and hL,Lo
calculated from Eqs. 12 and 14
𝑅𝑒𝐺 =6
𝑎
𝑈𝐺𝜌𝐺
𝜇𝐺
(1 +4
𝑎𝐷𝑐𝑜𝑙
)−1
Eq. 15 Eq. 16 Eq. 17
Determination of the interfacial area (a°) at the working point
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Step 1: (𝑎°
𝑎)
𝐿𝑜= 1.5(𝑎𝑑ℎ)−0.5 (
𝑈𝐿𝑑ℎ𝜌𝐿
µ𝐿)
−0.2
(𝑈𝐿
2𝑑ℎ𝜌𝐿
σ𝐿)
0.75
(𝑈𝐿
2
𝑔𝑑ℎ)
0.45
in which UL is the
working liquid velocity
Step 2: (𝑎°
𝑎)
𝐹𝑙= 7 (
𝑎°
𝑎)
𝐿𝑜(
σ𝐿
σ𝑊)
0.56
Step 3: (𝑎°
𝑎) = (
𝑎°
𝑎)
𝐿𝑜+ ((
𝑎°
𝑎)
𝐹𝑙− (
𝑎°
𝑎)
𝐿𝑜) × (
𝑈𝐺
𝑈𝐺,𝐹𝑙)
13
(with (𝑎°
𝑎)
𝐿𝑜and (
𝑎°
𝑎)
𝐹𝑙from steps 1
and 2)
Eq. 18 Eq. 19 Eq. 20
Table 5. Comparison of the experimental loading gas velocities (UG,Lo) at a given liquid load (UL) and L/G
ratio to the ones predicted using the Billet-Schultes correlations (Eqs 1-7). RE corresponds to the relative
error between the experimental and the theoretical loading gas superficial velocities. The liquid holdup
(hL,Lo) determined with the Billet-Schultes correlations is also provided.
UL (m h-1) L/G UG,Lo experimental (m s-1)
UG,Lo model (m s-1)
RE hL,Lo model
PDMS
3.06 1.02 0.64 0.64 0.0% 0.092
7.38 2.81 0.56 0.55 2.4% 0.150
12.36 5.50 0.48 0.48 0.5% 0.203
23.65 12.95 0.39 0.36 8.2% 0.280
Transformer oil 9.92 3.18 0.64 0.53 17.8% 0.160
16.14 5.92 0.56 0.46 17.6% 0.211
Lubricant
1.40 0.45 0.65 0.66 1.2% 0.083
2.69 1.00 0.56 0.59 5.0% 0.122
3.97 1.72 0.48 0.54 11.6% 0.158
5.23 2.53 0.43 0.50 15.3% 0.188
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Table 6. Comparison of the experimental flooding gas velocities (UG,Fl) at given liquid load (UL) and L/G
ratio to the ones predicted using the Billet-Schultes correlations (Eqs 8-11). RE corresponds to the
relative error between the experimental and the theoretical flooding gas superficial velocities. The liquid
holdup (hL,Fl) determined with the Billet-Schultes correlations is also provided.
UL (m h-1) L/G UG,Fl experimental (m s-1)
UG,Fl model (m s-1)
RE hL,Fl model
PDMS
17.81 3.59 1.06 0.92 13.4% 0.3927
23.65 6.24 0.81 0.80 1.5% 0.4145
29.82 8.72 0.73 0.73 0.1% 0.4293
36.27 13.83 0.56 0.58 3.5% 0.4445
Transformer oil
16.14 3.38 0.98 0.91 7.1% 0.3909
22.79 5.78 0.81 0.80 1.7% 0.4116
29.78 9.40 0.65 0.70 7.5% 0.4331
Lubricant
6.48 1.26 1.07 1.00 5.7% 0.4181
7.71 1.95 0.82 0.90 9.2% 0.4382
8.94 2.54 0.73 0.83 13.7% 0.4511
10.16 3.25 0.65 0.77 19.0% 0.4637
Table 7: Billet-Schultes constants determined and comparison with the ranges determined by the authors
for other packing materials.
a (m-
1) ε CP CLo Ch CFl
Flexipac® 500Z HC 500 0.95 0.462 1.68 1.50 1.73
Range of B-S correlations (Billet and Schultes, 1999)
80-545
0.68-0.985
0.25-1.33
2.45-3.79
0.482-1.90
1.55-3.02
Table 8: ARE between the experimental and theoretical (B-S correlations) pressure drops for the three
solvents studied in the pre-loading and loading zones.
PDMS 20 Transformer oil Lubricant
Both zones
Pre-loading zone
Loading zone
Both zones
Pre-loading zone
Loading zone
Both zones
Pre-loading zone
Loading zone
17.9% 31.8% 12.1% 19% 32% 13% 27% 36% 20%
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